# Evaluation of Rheology Measurements Techniques for Pressure Loss in Mine Paste Backfill Transportation

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Paste Backfill Preparations

_{3}content of tailing from Mine-B is higher. Also, there is no CO

_{2}and ZnO particle in Mine-A tailings. The particle size distribution (PSD) of tailings is shown in Figure 1 and Table 2. Mine-A tailings have a wider range of particle sizes than Mine-B. Mine B tailings are very fine, with 80% of the material passing 20 µm while the cumulative passing of Mine-A is only 45%. Particle sizes have a significant impact on the pressure drop across a pipe and are dependent on solid fraction and flow rate. Particles of larger size decrease the void space in the backfill, and, therefore, porosity. Coarser tailings have larger inter-particle spaces in comparison to finer tailings [40,41]. The mine-B curve has a steeper grade than Mine-A, indicating a narrower size range.

## 3. Theory and Methods

#### 3.1. Rotational Rheometer

#### 3.2. Cup and Bob Viscometer

^{−1}. The angular velocity varies from 0 to 25 rad/s with maximum torque of 0.025 Nm. Two sensors, MV DIN and SV II, were used in this test with two different types of containers. The first is a standard cup attachment and the second a cup with a height and diameter that is at least twice that of the bob [12]. The second cup is referred to as an infinite cup and aims to minimize the wall slip effects. Minor modifications were made in the shear rate calculation to account for the infinite cup. The slope of a plot between the natural log of angular velocity and shear stress at the bob was determined. This slope was used to obtain a modified shear rate, as shown in Equation (3).

#### 3.3. Vane Rheometer

#### 3.4. Slump Test

#### 3.5. Flow Loop Test

## 4. Results and Discussion

#### 4.1. Yield Stress

#### 4.2. Plastic Viscosity

#### 4.3. Statistical Analysis

## 5. Conclusions

- i.
- Slump tests overpredicted the Bingham yield stress for the finer Mine-B tailings but showed good agreement with vane for the coarser Mine-A tailings. The predictions made using the smallest 3-in mold had the least errors as statistical analyses while testing coarse paste backfill. MVDIN bob in an infinite cup showed the least errors while testing the finer Mine-B tailings.
- ii.
- FL100 vane tests showed moderate agreement with the loop test data for both sets of mine tailings. The effects of wall-slip reduced by the vane compared to smooth cylinders using MVDIN cup and bob tests were not profound in the tests. Good agreement was seen between FL100 vane and MVDIN cup and bob tests.
- iii.
- The infinite cup did not show a discernible superiority over the standard cup. However, the smaller SVII bob in the infinite cup has a better agreement for both Bingham yield stress and Bingham plastic viscosity over the MVDIN bob in the infinite cup.
- iv.
- The MVDIN standard cup had the least errors while predicting Bingham plastic viscosity for finer Mine-B tailings, as well as coarser Mine-A tailings.
- v.
- Higher particle size gives rise to a higher Bingham yield stress and viscosity.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Schematic representation of different rheometer geometries; (

**a**) cone and plate, (

**b**) concentric—cup and bob, (

**c**) parallel plate.

**Figure 5.**Schematic arrangement showing the initial and final stress distribution of the cylindrical mold slump test [25].

**Figure 6.**The flow loop test experimental apparatus (all dimensions are in mm). PD—positive displacement pump; HP—hopper; P1, P2, P3, and P4—pressure gauges; HE—heat exchanger; FM—flow meter.

**Figure 7.**Bingham yield stresses for (

**a**) Mine-A at 15 °C; (

**b**) Mine-A at 25 °C; (

**c**) Mine-A at 35 °C; (

**d**) Mine-B at 15 °C; (

**e**) Mine-B at 25 °C; and (

**f**) Mine-B at 35 °C.

**Figure 8.**Bingham plastic viscosity for (

**a**) Mine-A at 15 °C; (

**b**) Mine-A at 25 °C; (

**c**) Mine-A at 35 °C; (

**d**) Mine-B at 15 °C; (

**e**) Mine-B at 25 °C; and (

**f**) Mine-B at 35 °C.

Oxide | Mine-A | Mine-B | Oxide | Mine-A | Mine-B |
---|---|---|---|---|---|

CO_{2} | - | 0.88% | K_{2}O | 3.46% | 2.70% |

Na_{2}O | 3.32% | 1.50% | CaO | 5.67% | 6.52% |

MgO | 3.26% | 3.97% | TiO_{2} | 0.57% | 0.64% |

Al_{2}O_{3} | 18.64% | 17.67% | MnO | 0.15% | 0.13% |

SiO_{2} | 54.79% | 49.02% | Fe_{2}O_{3} | 6.75% | 9.15% |

SO_{3} | 2.83% | 7.29% | ZnO | - | 0.15% |

Parameter | Mine-A | Mine-B |
---|---|---|

d80 | 60 µm | 20 µm |

d50 | 25 µm | 10 µm |

d20 | 8 µm | 6.62 µm |

Cu | 10.1 | 3.5 |

Cc | 1.1 | 1.3 |

% <20 µm | 45% | 80% |

Specific gravity | 2.74 | 3.40 |

Test Label | Cup Type | Temperature (°C) | |||
---|---|---|---|---|---|

Standard | Infinite | 15 | 25 | 35 | |

Loop test | • | • | • | ||

MVDIN-Cup1 | • | • | • | • | |

MVDIN-Cup2 | • | • | • | • | |

MVDIN-Cup3 | • | • | • | ||

FL100-Vane1 | • | • | |||

FL100-Vane2 | • | ||||

3in-Slump1 | • | • | |||

4in-Slump1 | • | • | |||

6in-Slump1 | • | • | |||

6in-Slump2 | • |

Test Label | Cup Type | Temperature (°C) | |||
---|---|---|---|---|---|

Standard | Infinite | 15 | 25 | 35 | |

Loop test | • | • | • | ||

MVDIN-Cup1 | • | • | • | • | |

MVDIN-Cup2 | • | • | • | ||

MVDIN-Cup3 | • | • | • | ||

SVII-Cup4 | • | • | • | ||

FL100-Vane1 | • | • | • | ||

3in-Slump1 | • | • | • | ||

4in-Slump1 | • | • | • | ||

6in-Slump1 | • | • | • |

Description | MV DIN | SV II |
---|---|---|

Bob radius (Rb) | 19.36 mm | 10.10 mm |

Cup radius (Rc) | 21.00 mm | 21.00 mm |

Bob height (H) | 58.08 mm | 19.60 mm |

Description | FL 100 |
---|---|

Vane radius $({R}_{i}$) | 11.00 mm |

Standard cup radius $({R}_{o}$) | As per Equation (7) |

Vane height $(H\prime $) | 16.00 mm |

Model | Governing Expression | Interpretation |
---|---|---|

Root mean square error (RMSE) | $RMSE=\sqrt{\frac{{\sum}_{i=1}^{N}{\left({F}_{t}-{A}_{t}\right)}^{2}}{N}}$ | The smaller the errors, the better the model |

Mean absolute percent error (MAPE) | $MAPE=\frac{100}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\frac{\left|{F}_{t}-{A}_{t}\right|}{{A}_{t}}$ | The smaller the percentage error, the better the model |

Symmetric mean absolute percent error (SMAPE) | $SMAPE=\frac{200}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\frac{\left|{F}_{t}-{A}_{t}\right|}{\left|{F}_{t}+{A}_{t}\right|}$ | The smaller the percentage error, the better the model |

Akaike information criterion (AIC) | $AIC=N+Nlog\left(2\pi \right)+Nlog\left(\frac{RSS}{N}\right)+2\left(p+1\right)$ | The smaller the value, the better the model |

Bayesian information criterion (BIC) | $\begin{array}{cc}BIC=N+Nlog& \left(2\pi \right)+Nlog\left(\frac{RSS}{N}\right)\\ & +\left(logN\right)\left(p+1\right)\hfill \end{array}$ | The smaller the value, the better the model |

Rheology Test | RMSE | MAPE | SMAPE | AIC | BIC |
---|---|---|---|---|---|

Bingham yield stress | |||||

MVDIN standard cup and bob | 41.249 | 380.800 | 102.122 | 161.899 | 160.373 |

FL100 vane | 326.416 | 113.171 | 68.964 | 190.295 | 188.589 |

3in slump | 199.101 | 165.085 | 83.508 | 76.360 | 73.484 |

4in slump | 235.518 | 179.605 | 89.476 | 77.964 | 75.089 |

6in slump | 338.703 | 239.278 | 104.574 | 81.436 | 78.560 |

Bingham plastic viscosity | |||||

MVDIN Standard cup and bob | 0.256 | 240.080 | 93.455 | 25.045 | 23.520 |

Rheology Test | RMSE | MAPE | SMAPE | AIC | BIC |
---|---|---|---|---|---|

Bingham yield stress | |||||

MVDIN standard cup and bob | 53.642 | 40.862 | 54.591 | 126.916 | 125.001 |

MVDIN infinite cup and bob | 61.292 | 21.417 | 25.343 | 54.357 | 51.220 |

SVII infinite cup and bob | 56.292 | 38.419 | 48.264 | 59.088 | 56.088 |

FL100 vane | 88.563 | 100.430 | 71.147 | 102.776 | 100.467 |

3in slump | 220.953 | 150.203 | 81.409 | 116.275 | 113.967 |

4in slump | 279.756 | 179.837 | 91.663 | 119.760 | 117.451 |

6in slump | 416.296 | 240.154 | 107.715 | 125.629 | 123.320 |

Bingham plastic viscosity | |||||

MVDIN standard cup and bob | 0.083 | 23.419 | 23.537 | −2.349 | −4.264 |

MVDIN infinite cup and bob | 1.034 | 57.297 | 92.982 | 22.448 | 19.311 |

SVII infinite cup and bob | 0.500 | 68.024 | 107.564 | 17.182 | 14.045 |

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## Share and Cite

**MDPI and ACS Style**

Ahmed, H.M.; Bharathan, B.; Kermani, M.; Hassani, F.; Hefni, M.A.; Ahmed, H.A.M.; Hassan, G.S.A.; Moustafa, E.B.; Saleem, H.A.; Sasmito, A.P.
Evaluation of Rheology Measurements Techniques for Pressure Loss in Mine Paste Backfill Transportation. *Minerals* **2022**, *12*, 678.
https://doi.org/10.3390/min12060678

**AMA Style**

Ahmed HM, Bharathan B, Kermani M, Hassani F, Hefni MA, Ahmed HAM, Hassan GSA, Moustafa EB, Saleem HA, Sasmito AP.
Evaluation of Rheology Measurements Techniques for Pressure Loss in Mine Paste Backfill Transportation. *Minerals*. 2022; 12(6):678.
https://doi.org/10.3390/min12060678

**Chicago/Turabian Style**

Ahmed, Haitham M., Bhargav Bharathan, Mehrdad Kermani, Ferri Hassani, Mohammed A. Hefni, Hussin A. M. Ahmed, Gamal S. A. Hassan, Essam B. Moustafa, Hussein A. Saleem, and Agus P. Sasmito.
2022. "Evaluation of Rheology Measurements Techniques for Pressure Loss in Mine Paste Backfill Transportation" *Minerals* 12, no. 6: 678.
https://doi.org/10.3390/min12060678